Geodesic
A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum
Studia Mathematica, Tome 121 (1996) no. 2, pp. 167-183

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s}(T) = {x ∈ X : lim_{s→∞} ∥T(s)x∥ = 0}$. Then $X_{s}(T)$ is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then $X_{s}(T)$ is the annihilator of the unitary eigenvectors of T*, and $lim_{s} ∥T(s)x∥ = inf{∥x-y∥ : y ∈ X_{s}(T)}$ for each x in X.
DOI : 10.4064/sm_1996_121_2_1_167_183
Keywords: contraction semigroup, unitary spectrum, unitary eigenvector trajectory, asymptotic stability, trivially asymptotically stable, countable, spectral synthesis

Charles J. K. Batty 1 ; Zdzisław Brzeźniak 1 ; David D. Greenfield 1

1 
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Charles J. K. Batty; Zdzisław Brzeźniak; David D. Greenfield. A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum. Studia Mathematica, Tome 121 (1996) no. 2, pp. 167-183. doi: 10.4064/sm_1996_121_2_1_167_183

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